 
Summary: Assignment
December 1, 2002
1. Create two random, linearly separable data clouds in R 2 You can do this
as follows (or do your own thing): let f(x; y) = 2x + 5y 2 denote a line
which passes through the unit square [0; 1] 2 (verify this). Then generate
some random data (x; y), in [0; 1] 2 and assign the points to the two classes
depending on the sign of f(x; y).
Use the perceptron algorithm to locate a separating line.
Try this with a small set of data, so the line will be easy to locate (i.e., so
the perceptron algorithm will have an easy job of it), and a larger set of
data so the line will be harder to locate (i.e., the algorithm will take a lot
longer).
Report on the eÆcacy of the perceptron algorithm.
2. Use the data you have developed for digits' features (the subwindows'
blackpixels sums) for two (or more digit categories), and test the sepa
rating ability of a hyperplane determined by the pseudoinverse. (By test
I mean create the confusion matrix.)
3. Add to the 16element feature set (of the previous problem) the products
of pairs of the features, giving 16 +
